Lloyds TSB claims six million customers currently use its Internet banking service.
According to the research organisation Datamonitor, European adoption of Internet banking is set to reach 75 million users by 2005.
A survey conducted by the organisation, eBanking Technology in Europe 2001, predicts that banking technology spending in Europe will more than double between 2000 and 2005, rising from £1.9bn this year to almost £3.5bn by 2005.
But financial institutions hoping to shed jobs as a result of this investment in new delivery channels may be disappointed.
The building society Nationwide, which prides itself on offering new delivery channels, said: "Internet banking take-up is a drawn-out process.
"There are still millions of people in the UK who don't have access to computers or have no interest in Internet banking, and we see that continuing. It would take an overnight leap in customer acceptance for Internet banking to have that kind of effect [job losses in banks]."